A box and one force vector, F1 is shown. F1 = + 10 N. If the mass of the box is 3 kg, what is the magnitude and direction of a force, F2, that would need to be applied if the box was to have an acceleration of + 2 m/s 2 in the horizontal direction. (Indicate direction by including a plus or minus sign in front of the magnitude).
Sorry, F1 is not shown here.
To find the magnitude and direction of the force F2, we can use Newton's second law, which states that the force acting on an object is equal to the product of its mass and acceleration. Mathematically, it can be expressed as:
F = m * a
Here, F is the force, m is the mass of the object, and a is the acceleration.
Given:
Mass of the box, m = 3 kg
Acceleration of the box, a = +2 m/s^2 (positive since it is in the horizontal direction)
We're looking for the force F2, so rearranging the equation, we have:
F2 = m * a
Substituting the given values, we get:
F2 = 3 kg * (2 m/s^2)
F2 = 6 N
Therefore, the magnitude of the force F2 is 6 N.
Since the box is experiencing a positive acceleration in the horizontal direction, the direction of the force F2 needs to be in the same direction. Hence, the direction of F2 is also positive in the horizontal direction.
So, the direction of the force F2 is (+6 N) in the horizontal direction.